Genome-wide association studies (GWAS) provide a new and powerful approach to investigate the effect of inherited genetic variation on risks of complex diseases. With recent advances in genotyping technology, genome-wide association studies are now becoming a reality. Data from GWAS are expected in an accelerated rate. Despite tremendous efforts in developing efficient algorithms for mapping complex diseases/traits, single-locus based approaches are still the primary method for GWAS. However, it is known that usually multiple genetic factors, environmental factors as well as their interactions play an important role in the etiology of complex diseases. Novel and practical approaches to simultaneously model multiple variables and their interactions from hundreds of thousands single nucleotide polymorphisms (SNPs) are greatly needed. In this project, we propose to develop efficient algorithms and practical statistical tools to address two important problems in the context of genome- wide association studies: multi-point analysis and multi-locus analysis. For multi-point analysis, our Dynamic Hidden Chain Markov Model (DHCMM) can jointly model historical recombination and muta- tions, haplotype structures and frequencies, and associations, which is expected to be more effective than existing approaches. For multi-locus analysis, we propose to use an advanced machine learning approach to jointly screen SNPs that are predictive of diseases. Our integrated software system MAVEN will facilitate management, analysis, visualization and results sharing of GWA data using cut- ting edge technologies. The true value of GWAS is pending the development of effective computational models and tools. We anticipate that this research project will greatly accelerate the understanding of the genetic architecture of complex diseases.